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GRADE: 8STATISTICS CHAPTER: 26AVERAGES - DEFINITIONS.Mean:- sum of the itemsnumber of items .Median :- It is the central value.Mode :- It is the frequently occurring number ORThe most common value.Range :- Difference between maximum value and minimum value.RAW DATA.Mean is total scores divided by number of scores.Median is the middle score. Median is given by n+12th value. Where n is the number of scores of raw data.Step 1: Arrange the scores in ascending or descending order.Step 2: Select the middle term.Step 3: For odd numbers it is the middle term only.Step 4: For even numbers it is the mean of the middle two numbers or terms.Mode is the most common score.Range is the difference between the highest and lowest score.Find the mean, median, mode and range for the given set of numbers:3, 6, 2, 5, 9, 2, 4.10, 8, 10, 10, 16, 7, 9, 10, 8, 9.13, 16, 12, 14, 19, 12, 14, 13.1.6, 2.4, 3.9, 1.7, 1.6, 0.2, 1.3, 2.0.4, 3, 4, 5, 2, 5, 4, 3.5, 7, 9, 12, 10, 8, 7, 9, 7, 8, 12, 7.DISCRETE GROUPED DATA.ScorexFrequencyfCumulative frequencyfxTotalMean =fxf .Median is given by N+12th value. Where N is the total frequency.Mode is the common score which is related to the highest frequency.Range is the highest score minus the lowest score.Find the mean, median, mode and range for each of the following frequency tables:The number of newspapers bought in one week by the occupants of each house in a particular road was recorded. The results are shown in this frequency table.No. of newspapers23456789Frequency93210121563 The frequency table given below shows the number of tickets bought per person for a football match.Number of tickets1234567Frequency250200100501031This table shows the results of counting the number of prickles per leaf on 50 holly leaves.Number of prickles123456Frequency4287209A six-sided dice was thrown 50 times. The table gives the number of times each score was obtained.Score123456Frequency78108512Three coins were tossed together 30 times and the number of heads per throw was recorded.Number of heads0123Frequency312105CONTINUOUS GROUPED DATA.Class intervalFrequencyfCumulative frequencyMid valuexfxTotalMid value or mid x is the middle of the group or class interval. It is found by adding the upper limit and the lower limit and dividing by 2. In other words it’s the average or mean of limits of the class interval.Mean is the same as x=fxf .Median also is N+12th value. It is the medial class. Where N is the total frequency.In this case mode is the modal class or group which belongs to highest frequency.Range is again the highest value minus the lowest value of the class interval.Estimate the mean, median, mode and range for each of the following frequency tables:Fifty boxes of peaches were examined and he number of bad peaches in each box was recorded, with the following result:No. of bad peaches per box0 – 45 – 910 – 1415 – 19Frequency 341141The table shows the result of a survey amongst 100 pupils on the amount of money each of them spent in the school tuck shop on one particular day.Amount ( pence )0 – 2425 – 4950 – 7475 – 99Frequency 26153821Twenty tomato seeds were planted in seed tray. Four weeks later the heights of the resulting plants were measured and the following frequency table was made:Height ( h cm )1≤h<44≤h<77≤h<1010≤h<13Frequency 25103The table below gives the duration of telephone calls recorded in a shop.Duration of a phone call( t minutes )0≤t<55≤t<1010≤t<1515≤t<20Frequency 2030105This table shows the age groups of the employees at a small factory.Age of employees ( n years )18≤n<2828≤n<3838≤n<4848≤n<5858≤n<68Frequency 4659413717HISTOGRAM.Class intervalC.I.FrequencyfClass widthc.w.Frequency densityf.d.10<x≤208100.820<x≤5015300.5To draw a histogram check the class interval, it must be continuous.Find the class width. It is upper limit minus the lower limit.Find the frequency density using the formula f.d=fc.w. .Take suitable scale for the x - and y - axis and label the axes.Draw the bars for the given class intervals. The bars should be touching one another.Draw a histogram to illustrate the frequency tables:The table shows the distribution of the times taken by 40 children to complete an obstacle race:Time ( t seconds )0≤t<4040≤t<5050≤t<6060≤t<70Frequency 815710The table shows the distribution of weights of 30 bags of chips from a fish and chip shop:Weight ( w grams )0≤w<5050≤w<6060≤w<7070≤w<80Frequency 48144The table gives the distribution of lengths of 50 blades of grass:Length ( h mm )40≤h<5050≤h<6060≤h<7070≤h<8080≤h<110Frequency 68121212The table shows the distribution of the ages of people boarding buses at the bus station between 0830 and 0900 one morning:Age (n years )0≤n<1010≤n<2020≤n<3030≤n<4040≤n<70Frequency 1020302015x-----------x----------x ................
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