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The weights (in kg) of 20 boys in a class are given. Prepare a frequency distribution table and find the range of the data.

Mathematics

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Answer

10 kg10 \text{ kg}

Step-by-step solution

8 steps

Here are the solutions to questions 48 to 50.

48. Weights (in kg) of 20 boys in a class are given below:
The given data is:
$48, 46, 50, 44, 50, 48, 44, 50, 42, 48$
$42, 46, 40, 44, 46, 48, 50, 42, 46, 44$

  • Prepare a frequency distribution table for the above data.
  1. List the unique weights in ascending order.

    The unique weights are $40, 42, 44, 46, 48, 50$.

  2. Count the frequency of each weight.

    • 40 kg40 \text{ kg}: 1
    • 42 kg42 \text{ kg}: 3
    • 44 kg44 \text{ kg}: 5
    • 46 kg46 \text{ kg}: 4
    • 48 kg48 \text{ kg}: 4
    • 50 kg50 \text{ kg}: 3 Total count: 1+3+5+4+4+3=201+3+5+4+4+3 = 20, which matches the number of boys.

    Here is the frequency distribution table:

    Weight (in kg)Frequency
    401
    423
    445
    464
    484
    503
    Total20
    • What is the range of the data?
  3. Identify the maximum and minimum values in the data.

    Maximum weight =50 kg= 50 \text{ kg}
    Minimum weight =40 kg= 40 \text{ kg}

  4. Calculate the range.

    Range=Maximum value−Minimum value\text{Range} = \text{Maximum value} - \text{Minimum value} Range=50 kg−40 kg=10 kg\text{Range} = 50 \text{ kg} - 40 \text{ kg} = 10 \text{ kg}

    The range of the data is 10 kg\boxed{10 \text{ kg}}.

    49. During a rainy season, students of a class made a count of the umbrellas, which students brought to the class on Monday, Tuesday, Wednesday, Thursday, Friday and Saturday. The count was as under:
    Monday: 25
    Tuesday: 20
    Wednesday: 10
    Thursday: 20
    Friday: 15
    Saturday: 30

    • Represent this information through a pictograph.
  5. Choose a suitable symbol and scale.

    The numbers are 25,20,10,20,15,3025, 20, 10, 20, 15, 30. All are multiples of 5.
    Let's use the symbol ☂️ to represent 5 umbrellas.
    Scale: ☂️ =5= 5 umbrellas

  6. Convert the counts into symbols.

    • Monday: 25÷5=525 \div 5 = 5 umbrellas ☂️☂️☂️☂️☂️
    • Tuesday: 20÷5=420 \div 5 = 4 umbrellas ☂️☂️☂️☂️
    • Wednesday: 10÷5=210 \div 5 = 2 umbrellas ☂️☂️
    • Thursday: 20÷5=420 \div 5 = 4 umbrellas ☂️☂️☂️☂️
    • Friday: 15÷5=315 \div 5 = 3 umbrellas ☂️☂️☂️
    • Saturday: 30÷5=630 \div 5 = 6 umbrellas ☂️☂️☂️☂️☂️☂️

    Here is the pictograph:

    DayNumber of Umbrellas
    Monday☂️☂️☂️☂️☂️
    Tuesday☂️☂️☂️☂️
    Wednesday☂️☂️
    Thursday☂️☂️☂️☂️
    Friday☂️☂️☂️
    Saturday☂️☂️☂️☂️☂️☂️
    Scale: ☂️ = 5 umbrellas

    50. The following are the details of number of students present in a class of 30 during a week. Represent it by a pictograph.

    DaysNumber of students present
    Monday24
    Tuesday26
    Wednesday28
    Thursday30
    Friday29
    Saturday22
    • Represent it by a pictograph.
  7. Choose a suitable symbol and scale.

    The numbers are 24,26,28,30,29,2224, 26, 28, 30, 29, 22. These numbers include odd and even values.
    Let's use the symbol 🧍 to represent 2 students. For odd numbers, we will use a half symbol.
    Scale: 🧍 =2= 2 students, and 🚹 =1= 1 student (half symbol)

  8. Convert the counts into symbols.

    • Monday: 24÷2=1224 \div 2 = 12 students 🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    • Tuesday: 26÷2=1326 \div 2 = 13 students 🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    • Wednesday: 28÷2=1428 \div 2 = 14 students 🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    • Thursday: 30÷2=1530 \div 2 = 15 students 🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    • Friday: 29=14×2+129 = 14 \times 2 + 1. So, 14 full symbols and 1 half symbol 🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🚹
    • Saturday: 22÷2=1122 \div 2 = 11 students 🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍

    Here is the pictograph:

    DayNumber of Students Present
    Monday🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    Tuesday🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    Wednesday🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    Thursday🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    Friday🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🚹
    Saturday🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍🧍
    Scale: 🧍 = 2 students, 🚹 = 1 student
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