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Given mid-values and frequencies, construct a continuous series by calculating class interval width, lower limits, and upper limits.

Mathematics

ScanSolve AI Answer

Step-by-step solution

3 steps

To construct a continuous series from mid-values, we first need to determine the class interval width and then calculate the lower and upper limits for each class.

Here is the given data:

Mid values152535455565Frequency201917624173\begin{array}{|c|c|c|c|c|c|c|} \hline \text{Mid values} & 15 & 25 & 35 & 45 & 55 & 65 \\ \hline \text{Frequency} & 20 & 19 & 17 & 62 & 41 & 73 \\ \hline \end{array}
  1. Calculate the class interval width (ii).

    The class interval width is the difference between any two consecutive mid-values.

    i=25−15=10i = 25 - 15 = 10

    So, the class interval width is 10.

  2. Calculate the lower limit (LL) and upper limit (UU) for each class.

    The lower limit (LL) and upper limit (UU) for a class can be found using the mid-value (MM) and half of the class interval width (i2\frac{i}{2}).
    Here, i2=102=5\frac{i}{2} = \frac{10}{2} = 5.
    The formulas are:

    L=M−i2L = M - \frac{i}{2} U=M+i2U = M + \frac{i}{2}

    For each mid-value:

    • For M=15M = 15: L=15−5=10L = 15 - 5 = 10 U=15+5=20U = 15 + 5 = 20 Class interval: 10−2010 - 20

    • For M=25M = 25: L=25−5=20L = 25 - 5 = 20 U=25+5=30U = 25 + 5 = 30 Class interval: 20−3020 - 30

    • For M=35M = 35: L=35−5=30L = 35 - 5 = 30 U=35+5=40U = 35 + 5 = 40 Class interval: 30−4030 - 40

    • For M=45M = 45: L=45−5=40L = 45 - 5 = 40 U=45+5=50U = 45 + 5 = 50 Class interval: 40−5040 - 50

    • For M=55M = 55: L=55−5=50L = 55 - 5 = 50 U=55+5=60U = 55 + 5 = 60 Class interval: 50−6050 - 60

    • For M=65M = 65: L=65−5=60L = 65 - 5 = 60 U=65+5=70U = 65 + 5 = 70 Class interval: 60−7060 - 70

  3. Construct the continuous series.

    Combine the calculated class intervals with their corresponding frequencies.

    Class IntervalFrequency10−202020−301930−401740−506250−604160−7073\boxed{ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 10 - 20 & 20 \\ 20 - 30 & 19 \\ 30 - 40 & 17 \\ 40 - 50 & 62 \\ 50 - 60 & 41 \\ 60 - 70 & 73 \\ \hline \end{array} }
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