Question

Fill in the blanks from the alternatives given in the bracket

1) ______ is a positional average.
(Mean/ mode/ median/ geometric)

2) The arithmetic mean of the following observation 4, 8, 12, 16, is ______.
(8, 10, 6, 12)

3) Cumulative frequency is needed while finding the ______ of the distribution.
(mode/ median/ average/ normal)

4) _______ is the item having highest frequency.
(mean/ mode/ median/ average)

5) The second quartile is known as _______.
(median/ lower quartile/ upper quartile/ none)

6) The values which divide the total number of observations into 10 equal parts are ______.
(Quartiles/ percentiles/ deciles/ none)

7) There are ______ deciles.
(7/ 8/ 9/ 10)

8) There are _____ percentiles.
(100/ 98/ 97/ 99)

9) The range of 10 20 30 40 is ______.
(15/ 30/ 10/ 40)

10) 25^th percentile is equal to ______.
(Ist quartile / 25 the quartile / 24 the quartile / 2nd quartile)

Answer 1

1. Median is a positional average.
Explanation
The median is usually the middlemost observation of any series; it is not based on all observations.

2. The arithmetic mean of the following observation 4, 8, 12, 16, is 10.
Explanation
Arithmetic mean

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{n} \\ \overline{X}=\frac{4+8+12+16}{4}=\frac{40}{4}=10 \end{gathered}$$

3. Cumulative frequency is needed while finding the median of the distribution.
Explanation
In case of calculation of median after arranging the data in ascending or descending order, the cumulative frequencies are calculated. We then add the simple frequency as ∑f ad denote as N. Median is then calculated as the value of the item corresponding to the ${\left(\frac{N}{2}+1\right)}^{th}$ item.

4. Mode is the item having highest frequency.
Explanation
Any observation occurring maximum number of times or most frequently in a series is the mode of that series. Thus, we can say that the mode is the item having the highest frequency.

5. Second quartile is known as median.
Explanation
The second quartile divides a series into two equal parts. Median, being the middlemost observation of any series, divides the series into two equal parts. Thus, the second quartile is also known as the median.

6. The values which divide the total number of observations into 10 equal parts are deciles.
Explanation
Deciles are the values that divide the data into 10 equal parts. For this, the data are first arranged in ascending order. Deciles then divide the data into 10 groups of equal size.

7. There are 9 deciles
Explanation
Since deciles divide the data into 10 equal groups. Therefore, there are 9 points in the entire series which break the data into 10 equal groups.

8. There are 99 percentiles.
Since percentiles divide the data into 100 equal groups. Therefore, there are 99 points in the entire series which breaks the data into 100 groups of equal size.

9. The range of 10 20 30 40 is 30.
Explanation
Range = Highest value – Lowest value
Highest value = 40
Lowest value = 10
Range = 40 – 10 = 30

10. 25^th percentile is equal to 1^st quartile.
Explanation
A quartile divides the data into 4 equal groups. Therefore, the 1^st quartile would mean 1/4^th of the entire data. Similarly, a percentile divides the data into 100 equal groups. Now, 25^th percentile would also mean 1/4^th of the entire data. Thus, 25^th percentile is equal to the 1^st quartile.