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Data Handling Test - 21

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Data Handling Test - 21
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  • Question 1
    1 / -0
    In a Zonal athletic long jump meet the distances jumped by $$10$$ atheletes are: $$205\:cm, 200\:cm, 275\:cm, 260\:cm, 259\:cm, 199\:cm, 252\:cm, 239\:cm, 228\:cm$$ and $$281\:cm$$. Find the arithmetic mean of the jumps.
    Solution
    Distances jumped by $$10$$ athletes (in $$cm$$): $$205, 200, 275, 260, 259, 199, 252, 239, 228$$ and $$281$$
    Mean $$= \cfrac{\text{Sum}}{\text{Number of athletes}}$$
    Mean $$= \cfrac{205 +200 +275 +260 +259 +199 +252 +239 + 228 + 281}{10}$$
    Mean $$= \cfrac{2398}{10}$$
    Mean $$= 239.8$$
  • Question 2
    1 / -0
    If the mean of $$7$$,$$9$$,$$11$$,$$13$$,$$x$$,$$21$$ is $$13$$, find the value of $$x$$.
  • Question 3
    1 / -0
    The ages of $$5$$ children are $$13, 15, 11, 9$$ and $$8$$ years respectively. The average age is
    Solution
    Average is the sum of the data values divided by the total number of values.
    Given that, $$13, 15, 11, 9, 8$$ are the ages of $$5$$ children.

    Therefore, average age $$=\dfrac{13+15+11+9+8}{5}=\dfrac{56}{5}=11.2$$
  • Question 4
    1 / -0
    The horizontal line in a bar graph is called:
    Solution
    In the Cartesian coordinate system, the horizontal reference line is called $$x$$-axis.
    Therefore, the horizontal line in a bar graph is called $$x$$-axis.
    Hence, option $$A$$ is correct.
  • Question 5
    1 / -0
    Find the median of the following data:
    $$5, 7, 9, 11, 15, 17, 2, 23$$ and $$19$$
    Solution
    Median is middle score in the ordered data.
    Here given data is $$5,7,9,11,15,17,2,23,19$$.
    Arranging them in order, we have
    $$2, 5, 7, 9, 11, 15,17,19,23$$
    Middle score is $$11$$.
    Hence, median is $$11$$.
  • Question 6
    1 / -0
    The mean of $$3, a+ 2, 8, 12, 2a -1$$ and $$6$$ is $$7$$, find the value of $$a$$.
    Solution
    Given, mean is $$7$$.
    Therefore, mean $$=\dfrac {3+a+2+8+12+2a-1+6}{6}$$
    $$\Rightarrow 7=\dfrac {30+3a}{6}$$
    $$\Rightarrow 42=30+3a$$
    $$\Rightarrow 3a=12$$
    $$\Rightarrow a=4$$
  • Question 7
    1 / -0
    The bar graph shows the number of cakes sold at a shop in four days. What is the difference in number of cakes between the highest and the lowest daily sale?

    Solution
    From the above bar graph, the  highest number of cakes sold is $$45$$ (i.e., on Sunday).
    and the lowest number of cakes sold is $$25$$ (i.e., on Monday).

    Therefore, the difference between the highest and lowest number of cakes $$=45-25=20$$.

    Hence, option $$A$$ is correct.
  • Question 8
    1 / -0
    Find the mode of:
    $$7, 7, 8, 10, 10, 11, 10, 13, 14$$
    Solution
    Mode is defined as the maximum number of times an observation appears in the whole set.
    Here, by observation, we get that $$10$$ is appearing the maximum (i.e. $$3$$) times and hence this is the mode.
  • Question 9
    1 / -0
    In a class test in English $$10$$ students scored $$75$$ marks $$12$$ students scored $$60$$ marks $$8$$ scored $$40$$ marks and $$3$$ scored $$30$$ marks the mode for their score is:
    Solution

    $$\textbf{Step -1: Defining mode.}$$
                      $$\text{In a given data set, the mode is the value that appears most often among every other values.}$$
                      $$\text{Given data set says, }$$
                      $$\text{10 Students scored 75 marks.}$$
                      $$\text{12 Students scored 60 marks.}$$
                      $$\text{8 Students scored 40 marks.}$$
                      $$\text{3 Students scored 30 marks.}$$
    $$\textbf{Step -2: Finding the mode of their score.}$$
                      $$\text{The mode of their score will be the marks occurring most often.}$$
                      $$\therefore \text{12 Students scored 60 marks.}$$
    $$\textbf{Hence, The mode of their score is 60. (Option C)}$$
  • Question 10
    1 / -0
    The median of the data 30, 25, 27, 29, 35, 38, 28 is _______.
    Solution
    Arrange the given data in ascending order.
    We have, $$25, 27, 28, 29, 30, 35, 38$$
    Median is $$29$$

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