Find the mean and variance for the data
x_i 92  93  97  98  102  104  109
f_i    3  2    3     2    6       3      3

Solution:

Let us draw the frequency table based on the given information:

xi	fi	fixi	(xi - x)	(xi - x)2	fi (xi - x)2
92	3	276	-8	64	192
93	2	186	-7	49	98
97	3	291	-3	9	27
98	2	196	-2	4	8
102	6	612	2	4	24
104	3	312	4	16	48
109	3	327	9	81	243
		2200			640

Here, N = 22 and ∑⁷_{i = 1} f_ix_i = 2200

Therefore,

Mean can be calculated as:

x = 1/N ∑⁵_{i = 1} f_ix_i

= 1/22 x 2200

= 100

Variance,

(σ²) = 1/n ∑¹⁰_{i = 1}(x_i - x)²

= 1/22 x 640

= 29.09

---

NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.2 Question 5

Find the mean and variance for the data  xi 92  93  97  98  102  104  109  fi    3  2    3     2    6       3      3

Summary:

The mean and variance for the given data are 100 and 29.09