2.02g Calculate mean and standard deviation

In a study of reaction times, 25 participants completed a test where their reaction times (in milliseconds) were recorded. The results are shown in the stem-and-leaf diagram below: 20 | 3 5 7 9 21 | 0 2 5 6 8 22 | 1 3 4 5 7 9 23 | 0 2 5 8 24 | 1 4 6 7 25 | 2 5 Key: 21 | 0 represents a reaction time of 210 milliseconds

1. State the median reaction time. [1]
2. Calculate the interquartile range of these reaction times. [2]
3. Find the mean and standard deviation of these reaction times. [3]
4. State one advantage of using a stem-and-leaf diagram to display this data rather than a frequency table. [1]
5. One participant completed the test again and recorded a reaction time of 195 milliseconds. Add this result to the stem-and-leaf diagram and state the effect this would have on:
   1. the median
   2. the mean
   3. the standard deviation
   [4]
6. Explain why the interquartile range might be preferred to the standard deviation as a measure of spread in this context [2]

In a study of reaction times, 25 participants completed a test where their reaction times (in milliseconds) were recorded. The results are shown in the stem-and-leaf diagram below: 20 | 3 5 7 9 21 | 0 2 5 6 8 22 | 1 3 4 5 7 9 23 | 0 2 5 8 24 | 1 4 6 7 25 | 2 5 Key: 21 | 0 represents a reaction time of 210 milliseconds

1. State the median reaction time. [1]
2. Calculate the interquartile range of these reaction times. [2]
3. Find the mean and standard deviation of these reaction times. [3]
4. State one advantage of using a stem-and-leaf diagram to display this data rather than a frequency table. [1]
5. One participant completed the test again and recorded a reaction time of 195 milliseconds. Add this result to the stem-and-leaf diagram and state the effect this would have on: a. the median b. the mean c. the standard deviation [4]
6. Explain why the interquartile range might be preferred to the standard deviation as a measure of spread in this context [2]

The marks of 24 students in a test had mean \(m\) and standard deviation \(\sqrt{6}\). Two new students took the same test. Their marks were \(m - 4\) and \(m + 4\). Show that the standard deviation of the marks of all 26 students is 2.60, correct to 3 significant figures. [3]

The masses, in kilograms, of 100 chickens on sale in a large supermarket were recorded as follows.

Mass (\(x\) kg)	\(1.6 \leqslant x < 1.8\)	\(1.8 \leqslant x < 2.0\)	\(2.0 \leqslant x < 2.2\)	\(2.2 \leqslant x < 2.4\)	\(2.4 \leqslant x < 2.6\)
Number of chickens	16	27	28	18	11

Calculate estimates of the mean and standard deviation of the masses of these chickens. [5]

The masses, in kilograms, of 100 chickens on sale in a large supermarket were recorded as follows.

Mass (\(x\) kg)	\(1.6 \leq x < 1.8\)	\(1.8 \leq x < 2.0\)	\(2.0 \leq x < 2.2\)	\(2.2 \leq x < 2.4\)	\(2.4 \leq x < 2.6\)
Number of chickens	16	27	28	18	11

Calculate estimates of the mean and standard deviation of the masses of these chickens. [5]

Chris plays for his local hockey club. In his first 20 games for the club, the mean number of goals per game he has scored is \(0.7\), with a standard deviation of \(0.9\). In the next 5 games he scores \(0, 1, 0, 2, 1\) goals.

1. Find the mean and standard deviation for the number of goals per game Chris has scored in all 25 games. [7]
2. A sponsor pays Chris £65 each time he plays for the club and a further £25 for each goal he scores. Find the mean and standard deviation of the amount per game he earns from the sponsor for all 25 games. [4]