The mode (correct to two decimal places) for the given data is: Class- interval Frequency 0-10 6 10-20 9 20-30 8 30-40 14 40-50 28 50-60 20 60-70 11 70-80 9
46.36
Step 1 — Modal class: The highest frequency is 28, so the modal class is 40-50, giving \(L=40,\ f_1=28,\ f_0=14,\ f_2=20,\ h=10\).
Step 2 — Apply the mode formula:
\[\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2}\times h\]
\[= 40 + \frac{28-14}{2(28)-14-20}\times 10 = 40 + \frac{14}{22}\times 10\]
\[= 40 + 6.3636\ldots \approx 46.36\]
Therefore the mode is 46.36.
Similar Questions
The average of 25 numbers is 36. If the average of first 13 numbers is 32 and that of the last 13 numbers is 39, then the 13th number is
Calculate the mode of the following frequency distribution
Seconds
51-55
56-60
61-65
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2
7
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The approximate harmonic mean of 8, 6, 12, 4 is:
The arithmetic mean of marks of the students for the given data is:
Marks
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For a data set with 24 observations given below, the median is:
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Important Questions from Measures of Central Tendency
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
The median of the following observations 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 is 58. If 92 is replaced by 99 and 41 by 43 in the above data. The new median is:
If the difference of mode and median is 36, then the difference of median and mean is:
In a Mathematics test 15 students scored 80 marks, 20 students scored 75 marks, 28 students scored 65 marks and 25 students scored 60 marks, mode of the score is:
If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
