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allsm [11]
3 years ago
11

A student records the number of hours that they have studied each of the last 23 days. They compute a sample mean of 2.3 hours a

nd a median of 2.5 hours. When they review their data, they notice that the maximum value was recorded as 10 hours and it should have been 14. they fix this error. When compare to origional dataset, did the IQR:______________.1. Increase2. Decrease3. Stayed the same4. There is no way to tell without actually seeing the data
Mathematics
1 answer:
natita [175]3 years ago
6 0

Answer:

the standard deviation increases

Step-by-step explanation:

Let x₁ , x₂, .   .   .  , x₂₃ be the actual data observed by the student

The sample means  = x₁  +  x₂  +  .   .   .  , x₂₃ / 23

= \frac{x_1 +x_2 +...x_2_3}{23}

= 2.3hr

⇒\sum xi =2.3 \times 23 = 52.9hrs

let x₁ , x₂, .   .   .  , x₂₃  arranged in ascending order

Then x₂₃ was 10  and has been changed to 14

i.e x₂₃ increase to 4

Sample mean  = \frac{x_1 +x_2 +...x_2_3}{23}

\frac{52.9hrs + 4}{23} \\\\= \frac{56.9}{23} \\\\= 2.47

therefore, the new sample mean is 2.47

2) For the old data set

the median is x_1_2(th) values

[\frac{n +1}{2} ]^t^h value

when we use the new data set only x₂₃ is changed to 14

i.e the rest all observation remain unchanged

Hence, sample median = [{x_1_2]^t^h value remain unchange

sample median = 2.5hrs

The Standard deviation of old data set is calculated

=\sqrt{\frac{1}{n-1} \sum (xi - \bar x_{old})^2 } \\\\=\sqrt{\frac{1}{22}\sum ( xi - 2.3)^2 }---(1)

The new sample standard sample deviation is calculated as

= \sqrt{\frac{1}{n-1} \sum (xi-2.47)^2} ---(2)

Now, when we compare (1) and (2)  the square distance between each observation xi and old mean is less than the squared distance between each observation xi and the new mean.

Since,

(xi - 2.3)²  ∑ (xi - 2.47)²

Therefore , the standard deviation increases

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MArishka [77]

Answer: B. -3 and 7

Step-by-step explanation:

To find the zeros, just move the constants to the other side,

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If the number is moved to the other side its sign becomes opposite

Hope it helps!

8 0
2 years ago
Caden exercises daily by walking on a treadmill. He sets the machine so that he will walk at a steady rate of 3.6 miles per hour
babunello [35]

Answer:

a) d = 3.6t

b) 10.8 miles

c) 1.2 hours

Step-by-step explanation:

For part a:

Slope of a line: y = mx + b

In this case, the equation would be: d = mt,

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Note: b = 0 in this case because when Caden starts walking on the treadmill, he hasn't really covered any distance yet.

Therefore, plugging in a speed of 3.6 miles per hour, the equation is:

d = 3.6t

For part b:

This is a simple instance of plugging in 3 hours for our t value.

Therefore, d = 3.6 (3)

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For part c:

In this case, we are given that d = 4.32 miles.

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Dividing both sides by 3.6, we get

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5 0
3 years ago
Two quadratic functions are shown.
slava [35]

Answer:

Option (1) is the correct option.

Step-by-step explanation:

Function 1,

f(x) = 4x² + 8x + 1

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     = 4(x² + 2x + 1) - 4 + 1

f(x) = 4(x + 1)² - 3

This graph opens up with the vertex or minimum point at (-1, -3)

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Function (2)

From the given table minimum value of the function is 0 at x = -1 or minimum point as (-1, 0)

Therefore, Function 1 has the least minimum value and its coordinates are (-1, -3)

Option (1) is the correct option.

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