Question

The following are the ages of all employees of a small company:

18, 56, 40, 40, 51,51 56, 45, 48, 49 ,70

a) Find the sample mean

b) Find the sample median

c) Find the sample mode

d) Find .the sample range

e) Find the lower and upper quartiles, and the sample interquartile range IQR Q1= Q3= IQR=

f) Display the data with a boxplot (with fences andwhiskers).

Calculate Fences:

g) Write a brief description of this data (symmetry, outliers).

h) Which is the better summary measure for these data, the mean or the median? Explain.

i) Find the approximate value of the 85th percentile. Give a brief interpretation of this percentile

k) If two data sets have the same range:

(i) the distance from the smallest to largest observations are the same in both sets

(ii) the smallest and largest observations are the same in both sets

(iii) both sets will have the same variance

(iv) both sets will have the same interquartile range

Answer 1

(a)  Sample mean = Sum of terms/ Numbers of terms

Sample mean =( 18+ 56+ 40+ 40 +51+ 51+ 56+ 45 +48 +49+ 70)/11 = 524/11 = 47.6334

(b) Median

The following data set:

18 56 40 40 51 51 56 45 48 49 70

The median of the data set is 49.

Explanation

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

18   40   40   45   48   49   51   51   56   56   70   

So, the median is 49 .

(c)

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

18   40   40   45   48   49   51   51   56   56   70   

Since 3 (40, 51, 56) values occurs 2 times, there is no mode for this data set.

(d) Range = max - min

Range = 70-18= 52

ANSWERED

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