Question

A survey of 23 retirees was taken. Among other things, the retirees were asked to report the age at which they retired. Here are those 23 ages (in years). 33, 47, 49, 49, 52, 58, 59, 59, 61, 64, 64, 65, 66, 66, 67, 67, 68, 69, 71, 71, 74, 74, 76 Frequency 10 10+ 4 2+ 01A 30 40 50 60 Age (in years) 70 80

Answer 1

(a) Answer is

None of the above

Note : As we know that only mode can take more than one value . But we can see that the histogram shows only one mode ( only one highest peak) , thus its unimodal . Mode cannot take more than one value.

(b) Answer is

MEAN

Note : We know that only mean is affected by extreme observations(as mean is the sum of all observations divided by number of observations) , therefore mean will be affected if 76 is replaced by 87. Median and mode are not affected by extreme observations , as median is the value which divides the data in two halves , so its the value at the center . Mode is the observation which is repeated maximum number of times.

(c) Answer is

MEAN and MEDIAN

Note : We know that only mean is affected by extreme observations(as mean is the sum of all observations divided by number of observations) , therefore mean will be affected if smallest measurements were removed . Median is the central value, it depends on number of observation  . So if the smallest observation are removed , number of observation changes , thus median also changes.

(d) Median is greater

For left skewed data

mean < median < mode

For right skewed data

mean > median > mode