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# Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class

Height (in cm) Frequency Cumulative frequency

150 - 155 12 a

155 - 160 b 25

160 - 165 10 c

165 - 170 d 43

170 - 175 e 48

175 - 180 2 f

**Solution:**

Given, the data represents the frequency and cumulative frequency of heights of students in a class.

We have to find the values of the unknown entries a, b, c, d, e, f.

Height in cm |
Frequency |
Cumulative frequency |
Cumulative frequency calculation |

150 - 155 |
12 |
a |
a = 12 |

155 - 160 |
b |
25 |
a + b = 12 + b |

160 - 165 |
10 |
c |
12 + b + 10 = 22 + b |

165 - 170 |
d |
43 |
22 + b + d |

170 - 175 |
e |
48 |
22 + b + d + e |

175 - 180 |
2 |
f |
22 + b + d + e + 2 |

From the table,

12 + b = 25

b = 25 - 12

b = 13

22 + b = c

c = 22 + 13

c = 35

22 + b + d = 43

22 + 13 + d = 43

35 + d = 43

d = 43 - 35

d = 8

22 + b + d + e = 48

22 + 13 + 8 + e = 48

35 + 8 + e = 48

43 + e = 48

e = 48 - 43

e = 5

22 + b + d + e + 2 = f

22 + 13 + 8 + 5 + 2 = f

f = 50

Therefore, the values of unknown entries are a = 12, b = 13, c = 35, d = 8, e = 5, f = 50.

**✦ Try This: **Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class:

Height (in cm) | Frequency | Cumulative frequency |

150 - 155 | 16 | a |

155 - 160 | b | 27 |

160 - 165 | 18 | c |

165 - 170 | d | 48 |

170 - 175 | e | 54 |

175 - 180 | 5 | f |

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 14

**NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 12**

## Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class Height (in cm) Frequency Cumulative frequency 150 - 155 12 a 155 - 160 b 25 160 - 165 10 c 165 - 170 d 43 170 - 175 e 48 175 - 180 2 f

**Summary:**

The unknown entries in the distribution of heights of students in a class are a = 12, b = 13, c = 35, d = 8, e = 5, f = 50

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