Removing data values

Questions where one or more data values are removed from an existing dataset and the effect on mean and/or standard deviation must be calculated.

4 questions · Moderate -0.7

2.02f Measures of average and spread2.02g Calculate mean and standard deviation
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CAIE S1 2014 June Q4
6 marks Moderate -0.8
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.
CAIE S1 2004 November Q4
7 marks Moderate -0.3
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.
Edexcel S1 Q1
9 marks Moderate -0.8
  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)
Pre-U Pre-U 9794/3 2013 November Q5
8 marks Moderate -0.8
The table summarises 43 birth weights as recorded for babies born in a particular hospital during one week.
Birth weight (w kg)\(2.0 \leqslant w < 2.5\)\(2.5 \leqslant w < 3.0\)\(3.0 \leqslant w < 3.5\)\(3.5 \leqslant w < 4.0\)\(4.0 \leqslant w < 4.5\)
Frequency1691710
  1. State the type of skewness of the data. [1]
  2. Given that the lower quartile is 3.21 kg and the upper quartile is 3.96 kg, determine whether there are any babies whose birth weights might be regarded as outliers. [4]
  3. The mean birth weight was found to be 3.58 kg. However, it was discovered subsequently that the table includes the birth weight, 2.52 kg, of one baby that has been recorded twice. Find the mean birth weight after this error has been removed. [3]