Descriptive Statistics
What is the arithmetic average of a dataset called?
Mean
A researcher analyzes archived weather data from the past 10 years to study rainfall patterns. What type of study is this?
Retrospective
What shape is a normal distribution curve commonly referred to as?
Bell curve
What is interpolation used for?
Estimating values between known data points.
What is the general equation for a straight line used in regression?
y=mx+b
Which measure of central tendency is most affected by outliers?
Mean
An engineer monitors traffic flow at a busy intersection for one week without changing any signals or road conditions. What type of study is this?
Observational study
What percentage of data falls within one standard deviation of the mean in a normal distribution?
68%
What assumption is made when performing linear interpolation between two data points?
The change between the two points is linear (i.e., forms a straight line).
What does the slope represent in a linear regression model?
The rate of change of the dependent variable with respect to the independent variable.
What is the difference between the highest and lowest values in a dataset?
Range
A team tests three different battery materials by manufacturing and measuring the performance of each under identical conditions. What type of study is this?
Experimental Study
A manufacturer produces steel rods with diameters that follow a normal distribution. If the mean diameter is 10 mm and the standard deviation is 0.2 mm, what is the probability that a randomly selected rod has a diameter between 9.8 mm and 10.2 mm? (Do not use excel)
68%
What is the formula for linear interpolation between two points (x1,y1) and (x2,y2)?
y=y1+(x−x1)(y2−y1)/(x2−x1)
What is a residual in regression analysis?
The difference between the observed value and the predicted value from the regression line.
Given the dataset [8, 5, 9, 12, 10, 8], calculate the mean and standard deviation.
st dev = 2.3
A scientist wants to know if the average tensile strength of a new alloy exceeds 500 MPa. She tests 10 samples and compares the mean to the threshold. What kind of hypothesis test is this?
Single Hypothesis
A university tracks the number of hours students sleep per night. The data follows a normal distribution with a mean of 7 hours and a standard deviation of 1.5 hours.
What is the probability that a randomly selected student sleeps more than 10 hours?
Use the Excel formula:
=1 - NORM.DIST(10, 7, 1.5, TRUE)
Result: ≈ 0.0228 or 2.28%
Using the dataset below, estimate the temperature at 3.5 hours using linear interpolation.
Time Temperature
1 18
2 21
3 24
4 28
5 31
Use points at 3 hr (24°C) and 4 hr (28°C):
T=24+(3.5−3)(28−24)/(4−3)=26
Using the dataset below, calculate the best-fit line
Hours Practiced Performance Score
1 50
2 59
3 67
4 73
=slope(y-values,x-values) = 7.7
=intercept(y-values,x-values) = 43
y = 7.7*x +43
A dataset contains the following values representing hours studied per week:
[6, 8, 10, 12, 14, 16, 18]
Calculate the mean, median, mode, range, and standard deviation of this dataset.
mean = 12
median = 12
mode = none
range = 12
st dev = 4.3
A company compares the durability of two different packaging materials by testing 20 samples of each. What kind of hypothesis test is this?
Two Sample Hypothesis
A company tests the strength of a new composite material. The strength follows a normal distribution with a mean of 250 MPa and a standard deviation of 20 MPa.
What is the probability that a randomly selected sample has a strength between 230 MPa and 270 MPa?
Use the Excel formula:
=NORM.DIST(270, 250, 20, TRUE) - NORM.DIST(230, 250, 20, TRUE)
Result: ≈ 0.6827 or 68.27%
Using the dataset below, estimate the pressure at 6.2 seconds using linear interpolation.
Time Pressure
5 120
6 135
7 150
Use points at 6 s (135 kPa) and 7 s (150 kPa):
P=135+(6.2−6)(150−135)/(7−6)=138 kPa
The relationship between reaction rate R and temperature T is modeled by the exponential equation:
R=k⋅ezT
Linearize this equation and use the following data to find k and z.
T R
20 2
30 4
40 5
50 7
60 8
R=k⋅ezT
ln(R) = ln(k⋅ezT)
ln(R) = ln(k) + ln(ezT)
ln(R) = zT(ln(e)) + ln(k)
ln(R) = zT+ln(k)
Use ln(R) values as y values, we can find slope and y-intercept.
From there, z = slope = 0.03
and k = e(intercept) = 1.2