QuestionCalculate the estimated mean revision time for 120 students given the following time intervals and frequencies:
$0<t \leq 15$ : 0, $15<t \leq 30$ : 20, $30<t \leq 45$ : 50, $45<t \leq 60$ : 50.

Studdy Solution

STEP 1

Assumptions1. The table represents the distribution of time spent by120 students revising maths each week. . The time intervals are exclusive, meaning a student can only belong to one interval.
3. The frequency represents the number of students in each time interval.
4. We are asked to estimate the mean time spent revising maths.

STEP 2

To estimate the mean, we first need to find the midpoint of each time interval. This is done by adding the lower limit and the upper limit of each interval and dividing by2.
$Midpoint = \frac{Lower\, limit + Upper\, limit}{2}$

STEP 3

Calculate the midpoint for each time interval.
For the first interval, $0<t \leq15$ , the midpoint is $Midpoint = \frac{0 +15}{2} =7.5$ For the second interval, $15<t \leq30$ , the midpoint is $Midpoint = \frac{15 +30}{2} =22.5$ For the third interval, $30<t \leq45$ , the midpoint is $Midpoint = \frac{30 +45}{2} =37.5$ For the fourth interval, $45<t \leq60$ , the midpoint is $Midpoint = \frac{45 +60}{2} =52.5$

STEP 4

Next, we multiply each midpoint by its corresponding frequency to get the total time spent in each interval.
$Total\, time = Midpoint \\times Frequency$

STEP 5

Calculate the total time for each interval.
For the first interval, the total time is $Total\, time =7.5 \\times0 =0$ For the second interval, the total time is $Total\, time =22.5 \\times20 =450$ For the third interval, the total time is $Total\, time =37.5 \\times50 =1875$ For the fourth interval, the total time is $Total\, time =52.5 \\times50 =2625$

STEP 6

Now, add up all the total times to get the overall total time spent revising maths.
$Overall\, total\, time = \sum Total\, time$

STEP 7

Calculate the overall total time.
$Overall\, total\, time =0 +450 +1875 +2625 =4950$

STEP 8

Finally, to estimate the mean time spent revising maths, divide the overall total time by the total number of students (120).
$Mean\, time = \frac{Overall\, total\, time}{Total\, number\, of\, students}$

STEP 9

Plug in the values for the overall total time and the total number of students to calculate the mean time.
$Mean\, time = \frac{495}{120}$

STEP 10

Calculate the mean time spent revising maths.
$Mean\, time = \frac{4950}{120} =41.25$ The estimated mean time spent revising maths is41.25 minutes.

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QuestionCalculate the estimated mean revision time for 120 students given the following time intervals and frequencies:
$0<t \leq 15$ : 0, $15<t \leq 30$ : 20, $30<t \leq 45$ : 50, $45<t \leq 60$ : 50.

Studdy Solution

STEP 1

STEP 2

To estimate the mean, we first need to find the midpoint of each time interval. This is done by adding the lower limit and the upper limit of each interval and dividing by2.
$Midpoint = \frac{Lower\, limit + Upper\, limit}{2}$

STEP 3

STEP 4

Next, we multiply each midpoint by its corresponding frequency to get the total time spent in each interval.
$Total\, time = Midpoint \\times Frequency$

STEP 5

STEP 6

Now, add up all the total times to get the overall total time spent revising maths.
$Overall\, total\, time = \sum Total\, time$

STEP 7

Calculate the overall total time.
$Overall\, total\, time =0 +450 +1875 +2625 =4950$

STEP 8

Finally, to estimate the mean time spent revising maths, divide the overall total time by the total number of students (120).
$Mean\, time = \frac{Overall\, total\, time}{Total\, number\, of\, students}$

STEP 9

Plug in the values for the overall total time and the total number of students to calculate the mean time.
$Mean\, time = \frac{495}{120}$

STEP 10

Calculate the mean time spent revising maths.
$Mean\, time = \frac{4950}{120} =41.25$ The estimated mean time spent revising maths is41.25 minutes.

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QuestionCalculate the estimated mean revision time for 120 students given the following time intervals and frequencies: 0<t≤150<t \leq 150<t≤15: 0, 15<t≤3015<t \leq 3015<t≤30: 20, 30<t≤4530<t \leq 4530<t≤45: 50, 45<t≤6045<t \leq 6045<t≤60: 50.

Studdy Solution

STEP 1

STEP 2

To estimate the mean, we first need to find the midpoint of each time interval. This is done by adding the lower limit and the upper limit of each interval and dividing by2.Midpoint=Lower limit+Upper limit2Midpoint = \frac{Lower\, limit + Upper\, limit}{2}Midpoint=2Lowerlimit+Upperlimit​

STEP 3

STEP 4

Next, we multiply each midpoint by its corresponding frequency to get the total time spent in each interval.Total time=MidpointtimesFrequencyTotal\, time = Midpoint \\times FrequencyTotaltime=MidpointtimesFrequency

STEP 5

STEP 6

Now, add up all the total times to get the overall total time spent revising maths.Overall total time=∑Total timeOverall\, total\, time = \sum Total\, timeOveralltotaltime=∑Totaltime

STEP 7

Calculate the overall total time.Overall total time=0+450+1875+2625=4950Overall\, total\, time =0 +450 +1875 +2625 =4950Overalltotaltime=0+450+1875+2625=4950

STEP 8

STEP 9

Plug in the values for the overall total time and the total number of students to calculate the mean time.Mean time=495120Mean\, time = \frac{495}{120}Meantime=120495​

STEP 10

Calculate the mean time spent revising maths.Mean time=4950120=41.25Mean\, time = \frac{4950}{120} =41.25Meantime=1204950​=41.25The estimated mean time spent revising maths is41.25 minutes.

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QuestionCalculate the estimated mean revision time for 120 students given the following time intervals and frequencies:
$0<t \leq 15$ : 0, $15<t \leq 30$ : 20, $30<t \leq 45$ : 50, $45<t \leq 60$ : 50.

To estimate the mean, we first need to find the midpoint of each time interval. This is done by adding the lower limit and the upper limit of each interval and dividing by2.
$Midpoint = \frac{Lower\, limit + Upper\, limit}{2}$

Next, we multiply each midpoint by its corresponding frequency to get the total time spent in each interval.
$Total\, time = Midpoint \\times Frequency$

Now, add up all the total times to get the overall total time spent revising maths.
$Overall\, total\, time = \sum Total\, time$

Calculate the overall total time.
$Overall\, total\, time =0 +450 +1875 +2625 =4950$

Plug in the values for the overall total time and the total number of students to calculate the mean time.
$Mean\, time = \frac{495}{120}$

Calculate the mean time spent revising maths.
$Mean\, time = \frac{4950}{120} =41.25$ The estimated mean time spent revising maths is41.25 minutes.