**Question 1:** The scores in mathematics test (out of 25) of 15 students is as follows: (19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20) Find the mode and median of this data. Are they same?

**Answer:** The scores can be arranged as follows:

Score | Tally marks | No. of Students |
---|---|---|

5 | | | 1 |

9 | | | 1 |

10 | | | 1 |

12 | | | 1 |

15 | | | 1 |

16 | | | 1 |

19 | | | 1 |

20 | |||| | 4 |

23 | | | 1 |

24 | | | 1 |

25 | || | 2 |

Total | 15 |

Score occurring most number of times = 20

Hence, mode = 25

Median can be calculated as follows:

We have odd number of scores = 15

So, position of median

`=(text(Number of scores)+1)/(2)`

`=(15+1)/(2)=8`

The eighth score is shown below in bold:

5, 9, 10, 12, 15, 16, 19, **20**, 20, 20, 20, 23, 24, 25, 25

Hence, median = 20

In this case, median and mode are same.

**Question 2:** The runs scored in a cricket match by 11 players is as follows:

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Find the mean, mode and median of this data. Are the three same?

**Answer:** The scores can be arranged in ascending order as follows: (6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120)

Score | Tally makrs | No. of players |
---|---|---|

6 | | | 1 |

8 | | | 1 |

10 | || | 2 |

15 | ||| | 3 |

50 | | | 1 |

80 | | | 1 |

100 | | | 1 |

120 | | | 1 |

Total | 11 |

Mode = Score appearing most number of times = 15

Median can be calculated as follows:

We have odd number of scores = 11

So, position of median

`=(text(Number of scores)+1)/(2)`

`=(11+1)/(2)=6`

Sixth score = 15

Hence, median = 15

Arithmetic mean can be calculated as follows:

`text(Mean)=text(Sum of each observation)/text(Number of observations)`

=(6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120) ÷ 11

`=(429)/(11)=39`

**Question 3:** The weights (in kg.) of 15 students of a class are: 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

**Answer:** The weights can be arranged in ascending order as follows: (32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50)

Weight (in kg) | Tally marks | No. of students |
---|---|---|

32 | | | 1 |

35 | | | 1 |

36 | | | 1 |

37 | | | 1 |

38 | ||| | 3 |

40 | | | 1 |

42 | | | 1 |

43 | ||| | 3 |

45 | | | 1 |

47 | | | 1 |

50 | | | 1 |

Total | 15 |

(a) Find the mode and median of this data.

**Answer:** Mode = 38 and 43

Median = 40 (Eighth observation)

(b) Is there more than one mode?

**Answer:** There are two modes in this data.

**Question 4:** Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14

**Answer:**

Observations | Tally marks | No. of observations |
---|---|---|

12 | || | 2 |

13 | || | 2 |

14 | ||| | 3 |

16 | | | 1 |

19 | | | 1 |

Total | 9 |

Mode = 14

Median = 14 (fifth observation)

**Question 5:** Tell whether the statement is true or false:

(a) The mode is always one of the numbers in a data.

**Answer:** True; because mode shows the observation appearing for most number of times.

(b) The mean is one of the numbers in a data.

**Answer:** False; because mean is calculated after adding all the data and dividing the sum with total number of observations.

(c) The median is always one of the numbers in a data.

**Answer:** True; because median is the data in the middle.

(d) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

**Answer:** False: following is the explanation:

`text(Mean)= text(Sum of observations)/text(Number of observations)`

`=(6+4+3+8+9+12+13+9)/(8)`

`=(64)/(8)=8`

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