Find mean, median and mode of the following data.
Class intervals 0-4 5-9 10-14 15-19 20-24
Frequency 2 6 10 5 3
Answers
Answer:
mean 12.2
median 12
modal class 10-14 or mode 12 (whichever is done in class)
Step-by-step explanation:
Treat the values as though there were simply all the middle value in the respective classes. The central values are 2 (for the class 0-4), 7 (for the class 5-9), 12, 17 and 22.
So the for the mean, we have
mean = ( sum of value times frequency ) / ( sum of frequencies )
= ( 2×2 + 7 × 6 + 12 × 10 + 17 × 5 + 22 × 3 ) / ( 2 + 6 + 10 + 5 + 3)
= 317 / 26
≈ 12.2
For the median, we need to indentify the "middle". There are 2 + 6 + 10 + 5 + 3 = 26 values. Being even, there are two central values, and these are the 13th and 14th values (used 13 = 26 / 2). From the frequencies 2, 6, 10, 5, 3, the cumulative frequencies are 2, 8, 18, 23, 26. So once we've looked at the first class, we've looked at 2 values; after looking over the second class, we've passed by 8 values (we're looking for the 13th and 14th, so we're not there yet); after the third class, we've passes over 18 values ... that's it, we passed the 13th and 14th values --- they are in the third class and so are treated as value 12. For the median, we take the average of these two values, which is just 12. (This last step would matter if one were in one class and the other in the next class.)
So the median is 12.
For the mode, this is just asking which is most frequent. There are 10 values from the third class and this is the most frequently occurring one, so the third class is the "modal class". If you want a modal value, use the central value as with the median and median, so the answer would be 12.
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