Removing data values

4 The heights, \(x \mathrm {~cm}\), of a group of 28 people were measured. The mean height was found to be 172.6 cm and the standard deviation was found to be 4.58 cm . A person whose height was 161.8 cm left the group.

1. Find the mean height of the remaining group of 27 people.
2. Find \(\Sigma x ^ { 2 }\) for the original group of 28 people. Hence find the standard deviation of the heights of the remaining group of 27 people.

4 The ages, \(x\) years, of 18 people attending an evening class are summarised by the following totals: \(\Sigma x = 745 , \Sigma x ^ { 2 } = 33951\).

1. Calculate the mean and standard deviation of the ages of this group of people.
2. One person leaves the group and the mean age of the remaining 17 people is exactly 41 years. Find the age of the person who left and the standard deviation of the ages of the remaining 17 people.

1. The weight in kilograms, \(w\), of the 15 players in a rugby team was recorded and the results summarised as follows.

$$\Sigma w = 1145.3 , \quad \Sigma w ^ { 2 } = 88042.14$$

1. Calculate the mean and variance of the weight of the players. Due to injury, one of the players who weighed 79.2 kg was replaced with another player who weighed 63.5 kg .
2. Without further calculation state the effect of this change on the mean and variance of the weight of the players in the team. Explain your answers.
   (4 marks)