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Five people received the following scores on a personality test: 8,12,6,9 and 15. calculate the mode,median,mean and range of this distribution of scores.



Answer :

The set of scores has the following:

  1. Mean =  10
  2. Median = 6
  3. Mode = No mode
  4. Range = 7

Arrange the scores in ascending order

6,8,9,12,15

No. of observation = 5 (odd)

1) Mean:

[tex]Mean = \frac{Sum of observations}{No. of observations}[/tex]

[tex]Mean=\frac{6+8+9+12+15}{5}[/tex]

∴ Mean = 10

2) Median:

Since the no. of observations is odd, thus the median will be:

[tex]Median= \frac{(n+1)}{2}[/tex]

[tex]Median = \frac{5+1}{2 }[/tex]

∴ Median = 6

3) Mode:

For sets 6,8,9,12,15, there is no mode available because no value in the set appears more than once.

Hence, this set of values has no mode.

4)Range:

Range = Highest value - Lowest value

Range = 15 - 8

∴ Range = 7

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