**Category : **7th Class

It is defined as the value of variable which has highest frequency. The mode of data 10, 12, 14, 10, 14, 20, 30, 10, 25, 23, 10, 12 is 10, because it occurs most of the time. In the class - interval 1- 5, 5 is called upper limit and 1 is the lower limit.

** David throws a die 10 times and the following are outcomes 2, 5, 6, 6, 1, 5, 4,1, 4, 6, 5. The mean of the above observation is:**

(a) 3

(b) 4.5

(c) 5

(d) 45

(e) None of these

**Answer:** (b)

**Explanation **

\[mean=\frac{sum\,of\,observation}{Total\,number\,of\,observation}\]

\[=\frac{2+5+6+6+1+5+4+1+4+6+5}{10}=4.5\]

**If a, b, c, d, and e are five consecutive odd numbers, then their mean is:**

(a) b

(b) c

(c) e

(d) a

(e) None of these

**Answer:** (b)

**Explanation**

Let the consecutive odd numbers a, b, c, d and e are as follows

\[a=2x+1,b=2x+3,c=2x+5,\text{ }d=2x+7\]and\[~e=2x+9\]

\[\frac{(2x+1)+(2x+3)+(2x+5)+(2x+7)+(2x+9)}{5}=c\]

**The median of first five consecutive even numbers p, q, r, s and t is: **

(a) \[(q+s)\div 2\]

(b) p

(c)\[~(p+q)\div 2\]

(d) \[(p+q+r)\div 3\]

(e) None of these

**Answer:** (a)

** The mean, median and mode of the following data are respectively: 5, 17, 21, 21, 7,13,1, 3 **

(a) 10, 10, 21

(b) 11, 21, 2

(c) 11, 10, 21

(d) 11, 10, 5

(e) None of these

**Answer: (**c)

**Stuart performs his project work on the topic that the number of students likes soft drink of different flavours in a school. After collecting the data he wants to know the most flavoured soft drink which is liked by most of the students. Which central tendency makes his wish true? **

(a) Mean

(b) Row data

(c) Median

(d) Mode

(e) None of these

**Answer:** (d)

** Mean of Grouped Data **

Mean \[=\frac{\sum\limits_{i=\,1}^{n}{{{x}_{i}}{{f}_{i}}}}{\sum\limits_{i=1}^{n}{{{f}_{i}}}}\]where\[=\sum\limits_{i=1}^{n}{{{x}_{i}}{{f}_{i}}={{x}_{i}}{{f}_{i}}+{{x}_{2}}{{f}_{2}}+{{x}_{3}}{{f}_{3}}+{{x}_{4}}{{f}_{4}}+........}\]

And \[\sum\limits_{i=1}^{n}{{{f}_{i}}={{f}_{1}}+{{f}_{2}}+{{f}_{3}}+{{f}_{4}}+}.......\]

The difference between upper and lower limit of a class interval is called class size.

**Range **

The difference between maximum and minimum value of the observation is called range.

**Class Interval**

A data can be classified into different intervals for convenience to analyzing it. The interval in which variates lies is called class interval.

**Class Mark **

C.M. \[=\frac{1}{2}\](lower limit + upper limit)

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