The following is the data of pocket expenditure per week of 50 students in a class. It is known that the median of the distribution is ₹120. Find the missing frequencies.

Expenditure per week(in ₹) |
0 – 50 | 50 – 100 | 100 – 150 | 150 –200 | 200 –250 |

No. of students |
7 | ? | 15 | ? | 3 |

#### Solution

Let a and b be the missing frequencies of the class 50 – 100 and class 150 – 200 respectively.

We construct the less than cumulative frequency table as given below:

Expenditure per week (in ₹) |
No. of students (f) |
Less than Cumulative frequency(c.f.) |

0 – 50 | 7 | 7 |

50 – 100 | a | 7 + a |

100 – 150 | 15 | 22 + a ← Q_{2} |

150 – 200 | b | 22 + a + b |

200 – 250 | 3 | 25 + a + b |

Total |
25 + a + b |

Here, N = 25 + a + b

Since, N = 50

∴ 25 + a + b = 50

∴ a + b = 25 ............(i)

Given, Median = Q_{2} = 120

∴ Q_{2} lies in the class 100 – 150.

∴ L = 100, h = 50, f = 15, `(2"N")/4=(2xx50)/4` = 25,

c.f. = 7 + a

Q_{2 }= `"L"+"h"/"f"((2"N")/4-"c.f.")`

∴ 120 = `100+(50)/(15)[25-(7+"a")]`

∴ 120 – 100 = `10/3(25-7-"a")`

∴ 20 = `10/3(18-"a")`

∴ `60/10` = 18 − a

∴ 6 = 18 – a

∴ a = 18 − 6 = 12

Substituting the value of a in equation (i), we get

12 + b = 25

∴ b = 25 − 12 = 13

∴ 12 and 13 are the missing frequencies of the class 50 – 100 and class 150 – 200 respectively.