GSCE Mathematics Problem Solving Handling Data Higher Tier

Jacob manages a crisp factory. He wants to decide whether or not to use Lady Rosetta, Hermes or Saturna potatoes to make his crisps. The three varieties of potato all cost the same amount per kilogram. Here is some information about a typical bag of each of these varieties of potato. a) This table shows the distribution of weights of potatoes in a bag of 50 Lady Rosetta potatoes. Weight (w grams) Frequency 100 < w ≤ 200 15 200 < w ≤ 300 23 300 < w ≤ 400 8 400 < w ≤ 500 4 Jacob says that the smallest potato may weigh 100 g. Is he correct? Explain your answer. Think about your inequalities. Helping What does 100 < w ≤ 200 mean? hand

Answer Aron says that the smallest potato may weigh 100 g. Is he correct? Explain your answer. 100 < w ≤ 200 Consider the left hand side: Is the same as 100 < w w > 100 Which means that the weight is strictly greater than 100, not greater than or equal to 100, so this is not correct, the potato cannot weigh 100 g.

This histogram shows the distribution of weights (in grams), of potatoes in a bag of Hermes potatoes. How many potatoes were in the bag? Frequency = Helping frequency density x class width hand

Answer 100 x 0. 14 = 14 This histogram shows the distribution of weights (in grams), of potatoes in a bag of Hermes potatoes. How many potatoes were in the bag? 100 x 0. 22 = 22 100 x 0. 36 = 36 200 x 0. 14 = 28 14 + 22 + 36 + 28 = 100

This histogram shows the distribution of weights of potatoes in a bag of Hermes potatoes. Find the probability of selecting a potato which is at least 280 grams. Helping You have already worked out the frequency for 300 < w ≤ 500. You need to hand work this out for 280 < w ≤ 300.

Answer This histogram shows the distribution of weights of potatoes in a bag of Hermes potatoes. Find the probability of selecting a potato which is at least 280 grams. You need the area to the right of this line 28 20 x 0. 36 = 7. 2 280 7. 2 + 28 = 35. 2, so the probability of this is 35. 2/100 = 0. 352,

This table shows some information from a bag of 25 Saturna potatoes. Statistic Weight (grams) Mean 300 Median 320 Mode 330 Range 370 Jacob needs a variety of potato with a high average weight. He knows that large potatoes are best for making crisps. Use the information provided above to decide which of the three varieties of potato he should buy. Helping hand Use the information provided in the table above, together with the information you have already gathered. You may wish to discuss mean/median/mode/range/ probability of large potatoes

Jacob needs a variety of potato with a high average weight. He knows that large potatoes are best for making crisps. Use the information provided above to decide which of the three varieties of potato he should buy. If we consider the median value for each potato: Answer Lady Rosetta: 50 potatoes An estimate of the median is the 25 th value. This lies in the range 200 < w ≤ 300 Saturna: Statistic Weight (grams) Mean 300 Median 320 Mode 330 Range 370 Weight (w grams) Frequency 100 < w ≤ 200 15 200 < w ≤ 300 23 300 < w ≤ 400 8 400 < w ≤ 500 4 Values 115 The next 23 values i. e. 16 - 38 The 25 th value lies here

Hermes: 100 potatoes. An estimate of the median is the 50 th value. The 50 th value lies in here, so 200 < w ≤ 300 The next 14 22 36 values 1 -14 values 15 -36 37 -72 The median’s for the Lady Rosetta and Hermes potatoes lie between 200 < w ≤ 300. The Saturna potato has the highest median at 320 g, i. e. 50% of Saturna potatoes weigh at least 320 g. This would be the best potato to choose based on the median.

If we also consider the probability of choosing a potato which weighs at least 300 g, we can see that: Lady Rosetta: 8 + 4 = 12 potatoes weigh at least 300 g 12/50 = 24% Hermes: 28 potatoes weigh at least 300 g 28/100 = 28% Weight (w grams) Frequency 100 < w ≤ 200 15 200 < w ≤ 300 23 300 < w ≤ 400 8 400 < w ≤ 500 4 Saturna: At least 50% of the potatoes weigh more than 320 g (from the Median). Statistic Weight (grams) Mean 300 Median 320 Mode 330 Range 370 28 These results also show that there is a higher proportion of heavier potatoes with the Saturna variety. Jacob should buy Saturna potatoes.