STEM LEAF PLOTS A magazine did some testing

STEM & LEAF PLOTS

A magazine did some testing to see how long camera batteries lasted before they needed recharging. (Several cameras and test conditions were used). The results, measured in number of hours until a camera’s battery was flat, were as follows: 26, 32, 14, 10, 5, 34, 4, 7, 15, 17, 15, 22, 27, 20, 23, 36, 5, 56, 75

Organizing Battery Life Test Results Our first step in analyzing this data is to construct a Frequency Table of the results. 26, 32, 14, 10, 5, 34, 4, 7, 15, 17, 15, 22, 27, 20, 23, 36, 5, 56, 75 The Highest value is 75, and the lowest value is 4. This gives a Range of 75 - 4 = 71. Size of Intervals Range / 10 71 divided by 10 = 7. 1 = 7 **Seven is not the easiest of numbers to work with, and so we have decided to group our data into Groups of 10.

Frequency Table for Battery Life (hrs) 0 -9 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 Frequency Actual Values 4, 5, 5, 7

Frequency Table for Battery Life (hrs) 0 -9 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 Frequency Actual Values 4, 5, 5, 7 10, 14, 15, 17

Frequency Table for Battery Life (hrs) 0 -9 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 Frequency Actual Values 4, 5, 5, 7 10, 14, 15, 17 20, 22, 23, 26, 27

Frequency Table for Battery Life (hrs) 0 -9 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 Frequency Actual Values 4, 5, 5, 7 10, 14, 15, 17 20, 22, 23, 26, 27 32, 34, 3 6

Frequency Table for Battery Life (hrs) 0 -9 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 Frequency Actual Values 4, 5, 5, 7 10, 14, 15, 17 20, 22, 23, 26, 27 32, 34, 3 6 56

Frequency Table for Battery Life (hrs) 0 -9 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 Frequency Actual Values 4, 5, 5, 7 10, 14, 15, 17 20, 22, 23, 26, 27 32, 34, 3 6 56 75

Frequency Table for Battery Life (hrs) Frequency Actual Values 0 -9 4 10 – 19 5 20 – 29 5 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 3 0 1 4, 5, 5, 7 10, 14, 15, 17 20, 22, 23, 26, 27 32, 34, 3 6 56 75

Number of Hours 70 -7 9 9 -6 60 50 -5 9 9 -4 40 9 -3 30 10 9 1 - -2 0 -9 9 5 20 Number of Cameras Make a Histogram of the Data

Number of Hours 70 -7 9 9 -6 60 50 -5 9 9 -4 40 9 -3 30 10 9 1 - -2 0 -9 9 5 20 Number of Cameras Make a Histogram of the Data

Number of Hours 70 -7 9 9 -6 60 50 -5 9 9 -4 40 9 -3 30 10 9 1 - -2 0 -9 9 5 20 Number of Cameras Make a Histogram of the Data

Number of Hours 70 -7 9 9 -6 60 50 -5 9 9 -4 40 9 -3 30 10 9 1 - -2 0 -9 9 5 20 Number of Cameras Make a Histogram of the Data

Number of Hours 70 -7 9 9 -6 60 50 -5 9 9 -4 40 9 -3 30 10 9 1 - -2 0 -9 9 5 20 Number of Cameras Make a Histogram of the Data

Number of Hours 70 -7 9 9 -6 60 50 -5 9 9 -4 40 9 -3 30 10 9 1 - -2 0 -9 9 5 20 Number of Cameras Make a Histogram of the Data

Number of Hours 70 -7 9 9 -6 60 50 -5 9 9 -4 40 9 -3 30 10 9 1 - -2 0 -9 9 5 20 Number of Cameras Make a Histogram of the Data

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 Stem Leaf 40 – 49 50 – 59 56 60 – 69 70 - 79 75 A Stem and Leaf Plot is like a “T” chart.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 Stem Leaf 40 – 49 50 – 59 56 60 – 69 70 - 79 75 The stems are the intervals (groupings). Divide the actual values into the two digits that make up the number.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 Stem Leaf 40 – 49 50 – 59 56 60 – 69 70 - 79 75 For example, the number 4 is written as 04 The 0 is the stem, the 4 the leaf.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 40 – 49 50 – 59 56 60 – 69 70 - 79 75 Stem Leaf 0 1 2 3 4 5 6 7 4 5 5 7 Write the stem, then put the leafs in order.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 40 – 49 50 – 59 56 60 – 69 70 - 79 75 Stem 0 1 2 3 4 5 6 7 Leaf 4 5 5 7 0 4 5 5 7 Write the stem, then put the leafs in order.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 40 – 49 50 – 59 56 60 – 69 70 - 79 75 Stem 0 1 2 3 4 5 6 7 Leaf 4 5 5 7 0 2 3 6 7 Write the stem, then put the leafs in order.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 40 – 49 50 – 59 56 60 – 69 70 - 79 75 Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 5 4 2 4 5 7 5 5 7 3 6 7 6 Write the stem, then put the leafs in order.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 40 – 49 50 – 59 56 60 – 69 70 - 79 75 Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 5 4 2 4 5 7 5 5 7 3 6 7 6 6 Write the stem, then put the leafs in order.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 40 – 49 50 – 59 56 60 – 69 70 - 79 75 Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 5 4 2 4 5 7 5 5 7 3 6 7 6 6 5 Write the stem, then put the leafs in order.

Stem and Leaf Plots Battery Life (hrs) Actual Values 0 -9 4, 5, 5, 7 10 – 19 10, 14, 15, 17 20 – 29 20, 22, 23, 26, 27 30 – 39 32, 34, 36 40 – 49 50 – 59 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 5 4 2 4 5 7 5 5 7 3 6 7 6 6 5 56 1 3 = 13 60 – 69 70 - 79 Stem 75 Put a “key” at the bottom of the plot.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The minimum value is always the first term listed.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The minimum value is always the first term listed. The maximum is the last term listed.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The minimum value is always the first term listed. The maximum is the last term listed. To find the RANGE of the data subtract the minimum value from the maximum value.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The minimum value is always the first term listed. The maximum is the last term listed. To find the RANGE of the data subtract the minimum value from the maximum value. **Caution: Remember to use the entire term.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The minimum value is always the first term listed. The maximum is the last term listed. To find the RANGE of the data subtract the minimum value from the maximum value. **Caution: Remember to use the entire term. 75 – 4 = 71 NOT 5 – 4 = 1

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The minimum value is always the first term listed. The maximum is the last term listed. To find the RANGE of the data subtract the minimum value from the maximum value. **Caution: Remember to use the entire term. 75 – 4 = 71 NOT 5 – 4 = 1 So the range is 71

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MEDIAN is the middle term. Since these are now in order, we can just count to find the middle.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MEDIAN is the middle term. Since these are now in order, we can just count to find the middle. There are 19 values so the median is the 10 th term.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MEDIAN is the middle term. Since these are now in order, we can just count to find the middle. There are 19 values so the median is the 10 th term.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MEDIAN is the middle term. Since these are now in order, we can just count to find the middle. There are 19 values so the median is the 10 th term. The median for this data is 20 (not 0)

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MODE is the term that appears the most often.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MODE is the term that appears the most often. Using a stem and leaf plot, you must look at repeating numbers in each of the rows.

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MODE is the term that appears the most often. Using a stem and leaf plot, you must look at repeating numbers in each of the rows. There are two modes

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MODE is the term that appears the most often. Using a stem and leaf plot, you must look at repeating numbers in each of the rows. There are two modes

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MODE is the term that appears the most often. Using a stem and leaf plot, you must look at repeating numbers in each of the rows. There are two modes

Stem and Leaf Plots Stem 0 1 2 3 4 5 6 7 Leaf 4 0 0 2 6 5 1 3 = 13 5 4 2 4 5 7 5 5 7 3 6 7 6 The MODE is the term that appears the most often. Using a stem and leaf plot, you must look at repeating numbers in each of the rows. There are two modes 5 and 15 are both modes for this data