Question

The mean of 50 observations is 8. If another 10 observations with mean 20 are added to the
given data set, find the mean of the combined data set.
(a) 14
(b) 12
(c) 10
(d) 16​

Answer 1

The mean of the combined data set = 30.33.

• In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.
• The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

According to the given information,

The mean of 50 observations is 8. Then the sum of  50 observations is (50 × 8) = 400.

Again, the mean of 10 observations that has been added is 20.

Then, sum of these 10 observations = (20×10) = 200.

Sum of both observations = 400 + 200 = 600.

Now, mean of the combined data set = $\frac{600}{18} = 30.33$

Hence, the mean of the combined data set = 30.33.

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