# Frequency Distribution

- Data recorded as it is measured or received is called raw data.
- If we arrange raw data in increasing or decreasing order, we get a data array.
- The number of times a particular observation occurs is called its frequency.
- A table showing the frequency of various observations is called frequency distribution table.
- Tally marks ( | ) are useful for counting observations. We write tally marks in bunches of five like
- If number of observations is large, then grouping of data is done. Groups or classes are formed. The frequency table so prepared is called grouped frequency distribution table.
- The lower value of a class is called lower class limit and upper value is called upper class limit. Difference between these two is called class interval or class size or class width.
- Mid-point of class interval is called class mark.

## Exercise

- The shoe sizes of children in a class were found to be 5, 5, 4, 6, 5, 5, 5, 4, 4, 4, 7, 4, 5, 5, 4,
5, 6, 6, 4, 5.

(a) Construct data array for this.

(b) Construct tally chart.

(c) Construct simple frequency distribution table.

(d) Draw simple bar chart. - The marks obtained (out of 50) by 30 students in a class were 28, 31, 45, 03, 05, 18, 35,
46, 49, 17, 10, 28, 31, 36, 40, 44, 47, 13, 19, 25, 24, 31, 38, 32, 27, 19, 25, 28, 48, 15.

(a) Construct data array.

(b) Construct grouped frequency distribution table using groups 0-10,10-20, 20-30, 30-40, 40-50.

(c) What is the third class?

(d) What is the lower class limit of third class?

(e) What is the upper class limit of third class?

(f) What is the class interval of third class?

(g) What is the class mark of third class?

## Answers

**1.** (a) 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7

(b)

Value | Tally Marks |

4 | || |

5 | |||| |

6 | ||| |

7 | | |

(c)

Shoe size | Number |

4 | 7 |

5 | 9 |

6 | 3 |

7 | 1 |

Frequency distribution table (d) Simple bar chart showing shoe sizes of children in a class.

**2.**(a) 03, 05, 10, 13, 15, 17, 18, 19, 19, 24, 25, 25, 27, 28,

28, 28, 31, 31, 31, 32, 35, 36, 38, 40,44, 45, 46, 47, 48, 49.

(b) Grouped frequency distribution table showing marks obtained by students

Marks | 0 -10 | 10 -20 | 20 -30 | 30 -40 | 40 -50 |

Number of students | 2 | 7 | 7 | 7 | 7 |

(f) 10 (g) 25