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Statistics Test - 14

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Statistics Test - 14
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  • Question 1
    1 / -0
    If in a frequency distribution, the mean and median are 2121 and 2222 respectively, then its mode is approximately 
    Solution
    We have,
    Mode+2×Mean=3×MedianMode + 2 \times Mean =3\times Median
    Mode=3×Median2×Mean\Rightarrow Mode = 3 \times Median - 2\times Mean
    Given : Mean=21Mean=21 and Median=22Median =22
    Putting the given values, we get
    Mode=3×222×21=6642=24Mode =3\times 22-2\times 21=66-42=24
    Hence, option D is correct.
  • Question 2
    1 / -0
    Find mode from the following grouped frequency distribution table:
    Number of Trees PlantedNumber of Students
    0100-103030
    102010-206060
    203020-305050
    304030-407070
    405040-504040
    Solution
    N=30+60+50+70+40=250N=30+60+50+70+40=250
        N2=125\implies \cfrac{N}{2}=125
    Since, the highest frequency of students is 7070. So, 304030-40 is the modal group.
        L=30\implies L=30 
    Also, f0=50f_{0}=50,  frequency of the group before the modal group
    f1=70f_{1}=70, frequency of the modal group
    f2=40f_{2}=40, frequency of the group after modal group.
    h=10h=10, width of the group
    Then, Mode =L+f1f02f1f0f2×h=L + \cfrac{f_1 - f_0}{2f_1 - f_0-f_2}\times h
                         =30+70501405040×10=30+\cfrac{70-50}{140-50-40}\times 10
                         =30+2050×10=30+\cfrac{20}{50}\times 10
                         =30+4=34=30+4=34
    Hence, mode is 3434 trees.
  • Question 3
    1 / -0
     Class 5 - 10 10 - 1515 - 20 20 - 25 25 - 30  30 - 35 
     Frequency 515 10 14 
    The lower limit of the modal class of the following data is :
    Solution
    The highest frequency occurs in the class range 101510-15 that is 1515.
    Therefore,
    Modal Class: 101510-15
    Lower Limit: 1010
  • Question 4
    1 / -0
    Which of the following is a measure of central tendency?
    Solution
    A measure of central tendency is a typical value that is referred to as a representative of the whole data.
    The most common measures of central tendency are mean median and mode. 
  • Question 5
    1 / -0
    Median of 15,28,72,56,44,32,31,43 and 51 is 43.15, 28, 72, 56, 44, 32, 31, 43\ and\ 51\ is\ 43.
    Solution
    The terms are: 15, 28, 72, 56, 44, 32, 31, 43 and 51.
    Arranging them in ascending order: 15, 28, 31, 32, 43, 44, 51, 56, 72

    Since the total number of terms is odd that is 9, therefore the median will be the middle term that is the 5th term which is 43.
  • Question 6
    1 / -0
    A child says that the median of 3,14,18,20,53, 14, 18, 20, 5 is 1818. What concept does the child missed about finding the median?
    Solution
    To calculate the median of any data series. The data series has to be arranged in the ascending order. The child hasn't arranged the data series in ascending order.
  • Question 7
    1 / -0
    State true or false:
    The mode is the most frequently occurring observation.
    Solution
    The observation occurring the most number of times or which has highest frequency is called the mode.
    Thus, the given statement is true.
  • Question 8
    1 / -0
    3 median == mode + ................. mean.
    Solution

    A distribution in which the values of mean, median and mode coincide (i.e. mean = median = mode) is known as a symmetrical distribution. Conversely, when values of mean, median and mode are not equal the distribution is known as asymmetrical or skewed distribution. In moderately skewed or asymmetrical distribution a very important relationship exists among these three measures of central tendency. In such distributions the distance between the mean and median is about one-third of the distance between the mean and mode, as will be clear from the diagrams 1 and 2. Karl Pearson expressed this relationship as:

    Mode = mean - 3 [mean - median]

    Mode = 3 median - 2 mean

    3 Median = Mode + 2 Mean

  • Question 9
    1 / -0
    The modal value is the value of the variate which divides the total frequency into two equal parts.
    Solution
    False. Modal value is the value which occurs maximum number of times in the data.
  • Question 10
    1 / -0
    Median divides the total frequency into _____ equal parts.
    Solution
    The median of the data series is the middle term or the mean of the two middle terms.
    Hence, it divides the data series or the frequency of terms into two equal halves.
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