NIMCET 2026 — Mathematics PYQ

To find the sample mean and sample standard deviation, we use the following formulas for a data set $x_i$ with $n=7$ observations.

1. Calculate the Sample Mean ($\bar{x}$)

The mean is the sum of all observations divided by the number of observations:

$$\bar{x}=\frac{\sum x_i}{n}=\frac{14.5+15.2+16.8+17.1+15.9+16.3+14.7}{7}$$

$$\bar{x}=\frac{110.5}{7}\approx 15.7857\approx 15.79$$

2. Calculate the Sample Standard Deviation ($s$)

The sample standard deviation is calculated using the formula:

$$s=\sqrt{\frac{\sum (x_i-\bar{x}{)}^2}{n-1}}$$

First, calculate the squared deviations $(x_i-15.79{)}^2$:

• $(14.5-15.79{)}^2=(-1.29{)}^2=1.6641$

• $(15.2-15.79{)}^2=(-0.59{)}^2=0.3481$

• $(16.8-15.79{)}^2=(1.01{)}^2=1.0201$

• $(17.1-15.79{)}^2=(1.31{)}^2=1.7161$

• $(15.9-15.79{)}^2=(0.11{)}^2=0.0121$

• $(16.3-15.79{)}^2=(0.51{)}^2=0.2601$

• $(14.7-15.79{)}^2=(-1.09{)}^2=1.1881$

Sum of squares: $\sum (x_i-\bar{x}{)}^2=1.6641+0.3481+1.0201+1.7161+0.0121+0.2601+1.1881=6.2087$

Now, divide by $n-1=6$:

$$s=\sqrt{\frac{6.2087}{6}}=\sqrt{1.03478}\approx 1.017\approx 1.02$$

Conclusion

The sample mean is approximately $15.79$ and the sample standard deviation is approximately $1.02$. Therefore, the correct option is (b).