Question

The following number of goals were scored by a team in a series of 10 matches: 2, 3, 4, 5 , 0, 1, 3, 3, 4, 3. Find the mean, median and mode of these scores.

Answer 1

Hint: $ {\text{Mean}} = \dfrac{{{\text{Sum of terms}}}}{{{\text{Number of terms}}}} $ , we use this formula to calculate the mean. In order to find the median, we rearrange the given set of data in ascending order and then choose the middle term as median if these are odd terms. In the case of even numbers, we take the average of the 2 middle terms.
To find mode, we choose the most frequent value.

Complete step-by-step answer:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Consider $ {\text{Mean}} = \dfrac{{{\text{Sum of terms}}}}{{{\text{Number of terms}}}} = \dfrac{{2 + 3 + 4 + 5 + 0 + 1 + 3 + 3 + 4 + 3}}{{10}} $
 $ \Rightarrow Mean = \dfrac{{28}}{{10}} = 2.8 $
 $ \Rightarrow Mean = 2.8 $
Median: - Let us first rearrange the given series is ascending order, that is: - 0,1,2,3,3,3,3,4,4,5
Here we have even number of terms, so we choose the 2 middle terms, i.e 5th and 6th terms and find its average
 $ \therefore Median = \dfrac{{3 + 3}}{2} = \dfrac{6}{2} = 3 $
 $ \therefore Median = 3 $
Mode:- Consider the maximum repeated term in the series i.e, 3
 $ \therefore Mode = 3 $

Note: Keep in mind that the above method is followed for ungrouped data. The formula for mean, median and mode may vary for a grouped data. So identify whether the data is ungrouped or grouped and use the appropriate formula to obtain the correct answer.