Statistics

Total frequency: $N = 3+5+7+11+10+3+1 = 40$

Median

$\frac{N}{2}=\frac{40}{2}=20$

The cumulative frequency just greater than 20 is 26, so the median class is 60–70.

$L=60,\quad cf=15,\quad f=11,\quad h=10$

$\text{Median}=L+\frac{\frac{N}{2}-cf}{f}\times h$

$=60+\frac{20-15}{11}\times 10$

$=60+\frac{50}{11}=60+4.55=64.55$

$\boxed{\text{Median}=64.55}$

Mode

The highest frequency is 11, so the modal class is 60–70.

$L=60,\quad f_1=11,\quad f_0=7,\quad f_2=10,\quad h=10$

$\text{Mode}=L+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

$=60+\frac{11-7}{2(11)-7-10}\times 10$

$=60+\frac{4}{22-17}\times 10$

$=60+\frac{4}{5}\times 10=60+8=68$

$\boxed{\text{Mode}=68}$

Answer: Median = 64.55, Mode = 68.

Given:

Here $P_0, Q_0$ are base-year price and quantity, and $P_1, Q_1$ are current-year price and quantity. Prices are in Rs.

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1. Laspeyres Price Index Number

Formula:

$$P_{01}^{L}=\frac{\sum P_1Q_0}{\sum P_0Q_0}\times 100$$

Calculation table:

$$P_{01}^{L}=\frac{137}{110}\times 100$$ $$P_{01}^{L}=124.5454\approx \boxed{124.55}$$

So, by Laspeyres method, the Price Index Number is 124.55.

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2. Paasche Price Index Number

Formula:

$$P_{01}^{P}=\frac{\sum P_1Q_1}{\sum P_0Q_1}\times 100$$

Calculation table:

$$P_{01}^{P}=\frac{92}{74}\times 100$$ $$P_{01}^{P}=124.3243\approx \boxed{124.32}$$

So, by Paasche method, the Price Index Number is 124.32.

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Answer:

• Laspeyres Price Index Number = 124.55
• Paasche Price Index Number = 124.32