Sec 4 E-Math Averages & Spread topical questions

Find the mean of 3, 7, 8, 10 and 12.

Find the mode and the median of 5, 5, 6, 8, 9, 9, 9, 11.

The mean of six numbers is 8.4. Five of the numbers are 6, 7, 9, 10 and 11. Find the sixth number.

For the ordered list 8, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 26, 28, 30, 33, state the range.

Values 1, 2, 3 and 4 occur 3, 5, 6 and 6 times respectively. Find the mean.

Find the mean, the median and the mode of: 4, 6, 6, 9, 10, 13.

The mean of four numbers is 9.5. Three of the numbers are 7, 12 and 8. Find the fourth number.

The table shows waiting times: 0–10 min: 4 patients; 10–20 min: 10; 20–30 min: 6. (a) State the total number of patients. (b) Calculate the estimated mean waiting time.

1. (a)Total patients.[1]
2. (b)Estimated mean.[3]

Fifteen ordered masses in kg: 12, 14, 15, 16, 18, 19, 21, 22, 24, 25, 27, 29, 31, 33, 36. Find (a) the median, (b) the lower quartile, (c) the interquartile range.

1. (a)Median.[1]
2. (b)Lower quartile.[1]
3. (c)IQR.[2]

Find the standard deviation of 1, 3, 5, 7, 9, giving your answer correct to 3 significant figures.

A data set of 40 ordered values has minimum 12 and maximum 51. (a) Find the range. (b) State which single value the 20th percentile is read from, given that its position is 8.2.

1. (a)Range.[1]
2. (b)Which value.[2]

Grouped delivery times (min): 10–20: a; 20–30: 12; 30–40: 8. The estimated mean is 23 minutes. (a) Show that a = 15. (b) State the total number of deliveries.

1. (a)Show a = 15.[3]
2. (b)Total deliveries.[1]

A data set is: 2, 4, 4, 6, 8, 10, 12, 26. (a) Find the mean. (b) Find the median. (c) Which average describes a typical value better here, and why?

Heights of 20 plants are grouped: 150–160 cm: 4 plants; 160–170 cm: 8; 170–180 cm: 6; 180–190 cm: 2. (a) Calculate an estimate of the mean height. (b) State which class contains the median, with a reason.

Two printers print the same document. Printer P: mean 8.0 s per page, SD 0.6 s. Printer Q: mean 7.6 s per page, SD 2.4 s. A teacher wants fast and predictable printing. Compare the printers and make a recommendation.

A data set has mean 20 and standard deviation 3. (a) State the new mean and new SD if 5 is added to every value. (b) State the new mean and new SD if every value is instead multiplied by 3.

1. (a)After adding 5.[2]
2. (b)After multiplying by 3.[2]

Ten delivery times (min): 2, 3, 3, 4, 4, 4, 5, 5, 6, 24. (a) Find the mean and median. (b) The 24 is a recording error. Recompute both averages without it. (c) Which average changed more, and why?

1. (a)With the 24.[2]
2. (b)Without the 24.[2]
3. (c)Which changed more.[1]

Scores are grouped: 0–10: 4; 10–20: 6; 20–30: 6; 30–40: 4. (a) Find the estimated mean. (b) Using calculator statistics mode on the midpoints and frequencies, find the estimated standard deviation, correct to 3 significant figures.

1. (a)Estimated mean.[2]
2. (b)Estimated SD.[3]

The mean of eight numbers is 15. One more number is added, and the mean of the nine numbers becomes 16. (a) Find the original total. (b) Find the new total. (c) Find the added number. (d) Must the added number have been larger than all eight original numbers? Explain.

Two workers pack boxes; five timed attempts each, in seconds. Worker A: 32, 34, 35, 36, 38. Worker B: 28, 32, 35, 38, 42. (a) Show that both have a mean time of 35 seconds. (b) Find each worker’s standard deviation, correct to 3 significant figures. (c) Which worker would you assign to a task needing consistent packing times? Justify.